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From: David Barrett-Lennard <dbl.domain.name.hidden>

Date: Tue, 4 Nov 2003 11:45:39 +0800

In the words of Tegmark, let's assume that the physical world is

completely mathematical; and everything that exists mathematically

exists physically.

I have been thinking along these lines since my days at university -

where it occurred to me that any alternative is mystical. However, the

problem remains to explain induction - ie the predictability of the

universe. Why is it that the laws of physics can be depended on when

looking into the future, if we are merely a "mathematical construction"

- like a simulation running on a computer. It seems to me that in the

ensemble of all possible computer simulations (with no limits on the

complexity of the "laws") the ones that remain well behaved after any

given time step in the simulation have measure zero.

Given the "source code" for the simulation of our universe, it would

seem to be possible to add some extra instructions that test for a

certain condition to be met in order to tamper with the simulation. It

would seem likely that there will exist simulations that match our own

up to a certain point in time, but then diverge. Eg it is possible for

a simulation to have a rule that an object will suddenly manifest itself

at a particular time and place. The simulated conscious beings in such

a universe would be surprised to find that induction fails at the moment

the simulation diverges.

In other words, at each time step in a simulation the state vector can

take different paths according to slightly different software programs

with special cases that only trigger at that moment in time. It seems

that a universe will continually split into vast numbers of child

universes, in a manner reminiscent of the MWI. However there is a

crucial difference - most of these spin off universes will have bizarre

things happen. It is difficult to see how a computable system can be

tamper proof. How can a past which has been well behaved prevent

strange things from happening in the future?

In the thread "a possible paradox", there was talk about a vanishingly

small number of "magical" universes where strange things happen.

However, it seems to me that the bigger risk is that a "normal" universe

like ours will be the atypical in the ensemble!

A possible argument is to invoke the anthropic principle - and suggest

that our universe is predictable in order for SAS's to evolve and

perceive that predictability. However, that predictability only needs

to be a trick - played on the inhabitants for long enough to develop

intelligence. There is no reason why the trick needs to continue to be

played.

I suggest that the requirement of a tamper-proof physics is an extremely

powerful principle. For example, we deduce that SAS's only exist in

mathematical systems that aren't computable. In particular our

Universe is not computable.

- which is what Penrose has been saying.

I have assumed that non-computability coincides with being tamper-proof

but this is far from clear. For example, it is conceivable that the

Universe is a Turing machine running an infinite computation (cf

Tipler's Omega point), and "awareness" only emerges in the totality of

this infinite computation. Perhaps our awareness is a manifestation of

advanced waves sent backwards in time from the Omega Point!

I think it's important to distinguish between an underlying mathematical

system, and the formal system that tries to describe it. I think this

is a crucial distinction. For example, the real number system can be

defined uniquely by a finite set of axioms. Uniqueness is (formally)

provable - in the sense that it can be shown that an isomorphism exists

between all systems that satisfy the axioms. However the real numbers

are uncountably infinite - and therefore are very poorly understood

using formal mathematics - which is limited to only a countably infinite

set of statements about them. So formal mathematics should be regarded

as an imperfect and coarse tool which only gives us limited

understanding of a complicated beast! This is after all what Godel's

incompleteness theorem tells us.

It is not surprising that a computer will never exhibit awareness -

because it is merely using the techniques of formal mathematics, and not

tapping into the "good stuff".

- David

Received on Mon Nov 03 2003 - 22:47:33 PST

Date: Tue, 4 Nov 2003 11:45:39 +0800

In the words of Tegmark, let's assume that the physical world is

completely mathematical; and everything that exists mathematically

exists physically.

I have been thinking along these lines since my days at university -

where it occurred to me that any alternative is mystical. However, the

problem remains to explain induction - ie the predictability of the

universe. Why is it that the laws of physics can be depended on when

looking into the future, if we are merely a "mathematical construction"

- like a simulation running on a computer. It seems to me that in the

ensemble of all possible computer simulations (with no limits on the

complexity of the "laws") the ones that remain well behaved after any

given time step in the simulation have measure zero.

Given the "source code" for the simulation of our universe, it would

seem to be possible to add some extra instructions that test for a

certain condition to be met in order to tamper with the simulation. It

would seem likely that there will exist simulations that match our own

up to a certain point in time, but then diverge. Eg it is possible for

a simulation to have a rule that an object will suddenly manifest itself

at a particular time and place. The simulated conscious beings in such

a universe would be surprised to find that induction fails at the moment

the simulation diverges.

In other words, at each time step in a simulation the state vector can

take different paths according to slightly different software programs

with special cases that only trigger at that moment in time. It seems

that a universe will continually split into vast numbers of child

universes, in a manner reminiscent of the MWI. However there is a

crucial difference - most of these spin off universes will have bizarre

things happen. It is difficult to see how a computable system can be

tamper proof. How can a past which has been well behaved prevent

strange things from happening in the future?

In the thread "a possible paradox", there was talk about a vanishingly

small number of "magical" universes where strange things happen.

However, it seems to me that the bigger risk is that a "normal" universe

like ours will be the atypical in the ensemble!

A possible argument is to invoke the anthropic principle - and suggest

that our universe is predictable in order for SAS's to evolve and

perceive that predictability. However, that predictability only needs

to be a trick - played on the inhabitants for long enough to develop

intelligence. There is no reason why the trick needs to continue to be

played.

I suggest that the requirement of a tamper-proof physics is an extremely

powerful principle. For example, we deduce that SAS's only exist in

mathematical systems that aren't computable. In particular our

Universe is not computable.

- which is what Penrose has been saying.

I have assumed that non-computability coincides with being tamper-proof

but this is far from clear. For example, it is conceivable that the

Universe is a Turing machine running an infinite computation (cf

Tipler's Omega point), and "awareness" only emerges in the totality of

this infinite computation. Perhaps our awareness is a manifestation of

advanced waves sent backwards in time from the Omega Point!

I think it's important to distinguish between an underlying mathematical

system, and the formal system that tries to describe it. I think this

is a crucial distinction. For example, the real number system can be

defined uniquely by a finite set of axioms. Uniqueness is (formally)

provable - in the sense that it can be shown that an isomorphism exists

between all systems that satisfy the axioms. However the real numbers

are uncountably infinite - and therefore are very poorly understood

using formal mathematics - which is limited to only a countably infinite

set of statements about them. So formal mathematics should be regarded

as an imperfect and coarse tool which only gives us limited

understanding of a complicated beast! This is after all what Godel's

incompleteness theorem tells us.

It is not surprising that a computer will never exhibit awareness -

because it is merely using the techniques of formal mathematics, and not

tapping into the "good stuff".

- David

Received on Mon Nov 03 2003 - 22:47:33 PST

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